多变量化工过程系统的状态空间及其维数的判定准则

The Criterion for Dimensionality Analysis of the State Space of Chemical Processes

化工过程具有多变量、非线性和连续性的特征。状态空间是一种有效的描述过程状态和特征的方法。今从过程测量的基本因次关系出发,结合机理分析,提出了化工过程状态空间维数的判定准则。若系统单进单出的流股中包含i个独立物质组成,需要考虑j维几何尺寸因素,则系统可用一个维数是2+i+j的集中参数变量构成的状态空间来唯一确定。该准则可以用于确定主元分析方法(PCA)的主元数目。按照准则确定的空间维数选取主元可以完全描述线性系统的状态信息;对非线性系统,误差在可以接受的范围内。仿真案例中,PCA及过程独立变量分析和准则判定一致。在状态空间中采用PCA建立坐标描述过程的静态和动态特性,实现了过程状态的可视化,以及操作条件的多目标优化。

Based on the first principle and dimensional analysis, the criterion for determining the dimensionality of the state space was presented. The criterion points out that, for a lumped parameter and single-in and single-out(SISO)system, dimension number of the state space is 2 + i + j, where i stands for kinds of independent component in the process stream, j stands for dimension of geometry considered. The criterion is used in determination of the number of principal components (PCs) in the Principal Component Analysis (PCA). When the number of PCs is equal to the dimension number of state space, PCA represents linear system satisfactorily and represents non-linear system with reasonable accuracy. The proposed criterion was applied and demonstrated by a case study. The process static and dynamic descriptions were explored, the independent variables were analyzed, PCA was carried out. A visual optimization was proposed in the state space, in which its coordinates were constructed by PCA. Effective and visualized descriptions facilitate monitoring, control, and optimization of the chemical process.